Wing tip shapes, in particular for wings of aircraft, have been known for a long time and have already been examined in detail. The design of wing tip shapes is of essential importance in the development of present-day commercial aircraft and transport aircraft, which are operated at high transonic speeds (Mach 0.65 to Mach 0.95). The total drag of an aircraft wing operating in the transonic range is essentially comprised of wave drag, profile drag, induced drag and parasitic drag. The induced drag in turn essentially depends on the lift distribution on the wing, and on the wingspan. Therefore a reduction in the induced drag is most easily obtained by an increase in the wingspan. However, due to structural, industrial and operational constraints this is not possible to an unlimited extent.
One option for reducing the induced drag at a constant wingspan consists of the replacement of the planar tip shape of a wing with a non-planar shape.
A possible non-planar tip shape is a winglet, which is provided on the wing tip. Main geometrical parameters are the height, the taper ratio and the dihedral angle. The dihedral angle of the winglet can differ significantly from the dihedral angle of the wing and is typically constant or almost constant over the winglet span. If the dihedral angle of the winglet is constant or almost constant the winglet is denoted as planar or almost planar.
Generally speaking it has been shown that vertical winglets with an almost perpendicular transition between the wing and the winglet provide the most effective option for reducing the induced drag. However, the region of the transition from the wing to the winglet poses a problem, as in this region, due to interference effects in transonic flight, undesirable shock waves easily occur. The shock waves on the wing, which are a common and fundamental aspect of transonic aircraft operation, have a negative effect on the region of transition from the wing to the winglet, and in turn lead to an increase in the wave drag. Therefore, overall, the potential provided by vertical winglets cannot be fully utilised.
From U.S. Pat. No. 5,348,253, a wing tip shape for a wing of an aircraft is known, on which wing a winglet, provided on the wing tip, which winglet is essentially planar, is arranged at a transition region which extends from a connection on the wing to a connection on the winglet. The transition region, in which the local dihedral shape from the wing to the winglet makes a continuous transition, is in the shape of a circular arc with a radius of curvature that lies within narrow limits, which shape is determined by the height of the winglet, by said winglet's angle of inclination in relation to the wing span (cant angle), and by a constant parameter of curvature. This known wing tip shape is suitable for significantly reducing the induced drag; however, due to interference effects in the region of the circular-arc shaped transition from the wing to the almost planar winglet there is a tendency towards an undesired level of wave drag.
Furthermore, from DE 101 17 721 A1 or B4, corresponding to US 2002/0162917 A1 or U.S. Pat. No. 6,722,615 B2, a wing tip extension for an aircraft wing is known, which wing tip extension between a connection region for connection with the wing and the tip of the wing tip extension provides a continuous increase in the local dihedral, combined with a continuous increase in the sweep of both the leading edge and the trailing edge and a continuous decrease in the depth of the wing tip extension. As far as the angle of the local dihedral is concerned, it is stated that said angle is to increase from 0° to 10° in the connection region to the wing up to 45° to 60° at the tip of the wing tip extension. This known design of the wing tip extension results in a low level of interference and consequently low level of wave drag. However, the height that can be attained with this wing tip shape is limited, and there is little discretion in the selection of the design of the wing tip region if compared to the design of an added winglet.
Finally, from U.S. Pat. No. 6,484,968 B2 an aircraft is known with winglets provided on the ends of the wing, wherein the winglets follow an elliptical curve. The proposal of U.S. Pat. No. 6,484,968 B2 again defines a connection in which the curvature of the wing tip shape in the connection region to the wing is at its maximum and then along the wing span decreases, which is exactly contrary to the requirements defined later on, so that with this wing tip shape, too, undesired interference effects lead to an increase in the wave drag.